you're asking if your kick has a locker installed. there are only a few 'lockers' that fully engage, ie, 100% lock, that is the ARB air locker, a spool, or mini spool, and the lock right, or detroit lockers.
a lsd works on a different design, it allows for a certain amount of slip before a 'locking' sensation may be felt or encountered. an lsd consists of springs and clutch packs which cause increased friction between the clutch packs from the springs to limit slip.
if you have a trolley jack, jack the rear diff off the ground, so that both rear tyres are off the ground, remember to chock/block the front wheels so that it will not fall off the jack.
place the gearbox in 1st gear. (if you are checking the front, you will need to engage 4wd, and lock the front hubs if possible)
now spin either the left or rigth tyre any direction. observe what the other tyre does.
if it spins in the opposite direction, try spinning the tyre several more revolutions. if the effort is the same and does not increase, and the other tyre continues to spin in the opposite direction, then you do not have a locker installed.
with 1st gear selected, it will not be possible for the left and right tyres to turn in the same direction, ie, forward OR reverse.
with a lock right, the tyre you are turning should either produce a clicking/ratcheting noise as it unlocks and rides the internal driver, or it will lock and you will not be able to turn the tyre at all. if this happens, reverse the rotation of the tyre to see if it will unlock. by now, you should be able to conclude if your kick is equipped with a locker such as a lock right.
with some LSD diffs, it will act as a normal open unlocked diff until the clutch packs inside wind up and eventually lock both right and left tyres together.
if you spin the tyre, with 1st gear selected, and the other tyres spins in the opposite direction, have either someone hold the other tyre still and continue to spin the tyre on your side, if the effort increases to a point where it is hard(er) to turn, or unable to turn anymore, you may have a LSD installed.
it is also easy for lsd's to lose effectiveness after its clutches have worn out to a point where they are not able to cause enough friction to lock up both tyres together.
LSD's also have a level of tuning, depending on it you require it to be tight and lock up earlier, or if you dont mind it being left at standard specs and locking after ONE tyre has rotated a few revolutions.
you can also do this to the front to see if the front of your kick has a locker installed. but you need to make sure that the 4wd is engaged so the front drive shaft front the gear box to the front diff will not turn. also make sure the hubs are engaged, or locked.
chaining you kick up to a tree to see if it has lockers is almost a sure way to kill it in every respect.
also, accelerating hard on loose dirt or gravel will not give you a definate answer as to whether you have lockers or not, as a normal open diff will transfer power to the tyre with least grip, and on a loose surface both tyres on the driving axle will spin. also a kick is reasonably light in weight.
if you want to use this particular method, (only in 2wd), then position your kick where it will have its left tyres on the road or a hard non slippery surface, and the right tyres on dirt, or off the road. make sure the road a head is clear, and accelerate hard. this does not need to be redline in 1st gear, nor does it have to be all the way down the street.
observe what your kick does. if the tyre on the dirt spins ridiculously, and you move off reasonably slow, you do not have a locker.
if the tyre on the dirt does not spin, or the tyre on the road spins also, then you will have a locker of some sort fitted.
ultimately, the only way to be to be 100% sure, is to pull the carrier out of the diff housing and inspect.
